The present invention relates to an apparatus having a hardware architecture and to a method for calculating and encoding hologram data, as can be used for example for representing three-dimensional scenes (3D scenes) and objects using a holographic display.
The invention in particular also relates to an apparatus for optimized calculation of 2D sub-holograms for object points of a three-dimensional scene for a holographic display, and to a method for calculating a 2D sub-hologram for object points of a three-dimensional scene for a spatial light modulator (SLM), to an apparatus and to a method for encoding a hologram of a three-dimensional scene in a spatial light modulator, and to a pipeline for real-time calculation of holograms.
A holographic display of this type and a calculation method for calculating holographic data is described for example in the following publications: WO 2004/044659 A2, WO 2006/066919 A1, WO 2007/118842 A1, WO 2007/135165 A1, WO 2008/025839 A1, WO 2008/138979 A1 and WO 2011/121130 A9. The content of these publications is hereby incorporated in its entirety. These publications describe in particular the term sub-hologram and its meaning in detail, to which reference will be made in the following text. Said publications also describe what is meant by 1D and 2D encoding, that is to say one-dimensional or two-dimensional encoding of a (sub-)hologram.
Previous approaches have been based for example on utilization of the symmetry, in particular mirror symmetry, in the sub-hologram calculation, that is to say that only hologram values for one quadrant (i.e. in one quarter) of a 2D sub-hologram need to be calculated. The values of the remaining three quadrants are not explicitly calculated, but the calculated values of the first quadrant of the 2D sub-hologram are used to determine the values of the three remaining quadrants, specifically by obtaining or copying the values of the calculation result of the first quadrant of the 2D sub-hologram by way of a corresponding mirroring of the values of the first quadrant along the main axes of the 2D sub-hologram. What is meant by mirror symmetry is at least one axis symmetry and/or a point symmetry, where the point symmetry can relate in particular to the centerpoint of a sub-hologram SH.
Even with this, the complexity is still incredibly high; in the case of such 2D encoding, the complexity is higher, for example, compared to the 1D encoding by a factor of 100 and more, specifically in particular dependent on the pitch of the image elements (pixel pitch, center-to-center spacing of two image elements) of the spatial light modulator used for hologram representation—which spatial light modulator is also referred to as SLM—and the scene depth to be represented. What is meant by the pitch is in particular a size which is composed of the size of an image element (pixel size) and the respective spacing between two neighboring image elements (pixel spacing) of the spatial light modulator.
Such a method for calculating a 2D sub-hologram according to the prior art will now be described:
For each image element of the first quadrant of a 2D sub-hologram, the phase and the amplitude are calculated with which the light that is used to represent a three-dimensional scene is to be modulated or influenced by the spatial light modulator. The phase is here the result in particular of parameters such as the distance or the spacing between an object point to be represented and the spatial light modulator, and the pitch of the image elements (pixel pitch) (px, py), wherein px designates the pitch of the image elements in the x-direction and py designates the pitch of the image elements in the y-direction. The distance of an object point to be represented from the spatial light modulator will be designated in the following as focus (F). After the calculation of the polar coordinates, amplitude and phase, a very calculation-intensive step is subsequently carried out, the transformation of the phase and the amplitude in the Cartesian space with real and imaginary values. This is what permits the accumulation, that is to say the superposition, of the calculated 2D sub-hologram with other 2D sub-holograms in the sum hologram.
FIG. 1 gives a brief overview of the calculation of a 2D sub-hologram according to the prior art and of the calculation process for establishing the entire hologram of the three-dimensional scene to be represented, wherein, in addition to the above-mentioned parameters, φ is furthermore the phase value, A is the amplitude value of the respective image element, λ is the wavelength of the utilized light, SHw is the sub-hologram width and SHh is the sub-hologram height and b is the brightness of the object point.
The symmetry is utilized since the position of the image element (x, y) is incorporated as a square in the phase calculation. FIG. 2 clarifies this again.
Further principles for calculating holograms with 2D sub-holograms are known, for example, from the publications mentioned in the introductory part, and are therefore not explained further at this point.
The present invention is based on the object of specifying and developing an apparatus and a method of the type mentioned in the introductory part, with which the previously mentioned problems are overcome. In particular, the objective is to shorten the calculation time of a hologram for representing a three-dimensional scene and/or to reduce the calculation complexity of such a hologram as compared to the methods known from the prior art. Representing a three-dimensional scene in this case is to be read in the sense of reconstructing a three-dimensional scene.